You cannot reach the 6 * Vref, because the value of 6 * 1.024 = 6.144 exceeds the maximum voltage of an input-pin of 5.0V.
Just calculating 8192 / 6.144 * 5 = 6667 which gets near your observed value,
If you have Rail to Rail mode set, its actually not R-R performance. See input
range below for these settings. If you want real R-R performace you have to bypass
the input buffer, which means no G is available for the A/D front end. So your 1.3 V
X 4 = 5.2V in R-R mode is not accurate, as you can see.
Note the range when bypass is set is only 100 mV outside the rails, but good enough
for measuring power supply V or high side current sensing Rs.
Bob & Dana,
Thx a lot for your help, in fact the answer from Bob was the trigger to my miss-interpretation of the parameters for an input set upto 6*Vref.